Electronic structures of imidazolium-based ionic liquids

Electronic structures of ionic liquids formed by 1-buthyl-3-alkylimidazolium ion [C_nmim]⁺ (n = 4 and 8) with various inorganic and organic anions have been investigated by ultraviolet photoemission, X-ray photoemission, inverse photoemission and soft X-ray emission spectroscopies (SXES). The comparison of the calculated density of states with the observed spectra revealed that the molecular orbital energies of these ionic liquids are significantly affected by the electrostatic Madelung potential among the ions. The SXES results clearly show that the both highest occupied and lowest unoccupied states of [C₄mim]⁺PF₆⁻ are derived from the cation as a result of strong Madelung potential. On the other hand, the SXES results show the valence electronic structures of ionic liquids with larger anion molecules, [C_nmim]⁺Tf₂N⁻ and [C_nmim]⁺OTf⁻ are contributed from the both cation and anion.     

Inverse conductivity Problem with Internal Data

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This problem finds applications in multi-wave imaging, greedy methods to approximate parameter-dependent elliptic problems, and image treatment with partial differential equations. We first show that the inverse problem for smooth coefficients can be rewritten as a linear transport equation. Assuming that the coefficient is known near the boundary, we study the well-posedness of associated transport equation as well as its numerical resolution using discontinuous Galerkin method. We propose a regularized transport equation that allow us to derive rigorous convergence rates of the numerical method in terms of the order of the polynomial approximation as well as the regularization parameter. We finally provide numerical examples for the inversion assuming a lower regularity of the coefficient, and using synthetic data.     

一般超图的张量谱性质

将一致超图的逆Perron值的概念推广到了一般超图上,并证明了超图G连通的充要条件为其逆Perron值大于0。同时给出了一般超图G的二分宽度、等周数、离心率基于逆Perron值的一些下界。最后,讨论了张量的可奇染色问题,得到非负对称弱不可约张量A可奇染色的充要条件为A的拉普拉斯张量和无符号拉普拉斯张量有相同的的谱。     

Inverse transient radiation analysis in one-dimensional non-homogeneous participating slabs using particle swarm optimization algorithms

Particle Swarm Optimization (PSO) algorithms, including standard PSO, Stochastic PSO, and Multi-Phase PSO, are applied to solve the time-domain inverse transient radiation problems in the present research. Time-resolved transmittance and reflectance signals of four different measuring models serve as the measurement data, which estimate absorption, scattering coefficients, and geometric position within one-dimensional non-homogeneous media by inverse simulation. To check retrieval performances and accuracies of PSO-based approaches, four different inverse transient radiation cases are investigated to deal with one homogeneous layer, two-layer, three-layer, and continuous non-homogenous media. The influences of different searching ranges, swarm sizes, and maximum fly velocities on the fitness function of PSO are discussed. Meanwhile, the effects of measurement errors on the reconstruction accuracy are also investigated. All the results confirm that radiative parameters could be estimated accurately with measurement noise using PSO-based approaches.     

反传热问题及其在深冷处理传热分析中的应用

深冷处理作为一种新的材料处理工艺,越来越受到人们的关注,目前深冷处理使材料性能提高的机理尤其是与升降温过程的耦合关系等还尚未完全清楚,需开展更深入的研究,而传热分析是此方面研究的基础。反传热分析方法是研究深冷处理传热问题的一种可行方法。较为详细地叙述了反传热问题的定义及其求解方法,介绍了反传热在深冷处理传热分析中的初步应用,并对深冷处理中应用反传热方法存在的问题进行了探讨。     

反向PCR扩增问号赖型钩体重组质粒pDJH2插入片段

钩端螺旋体赖型赖株（Ｌ．ｉｎｔｅｒｒｏｇａｎｓＳｅｒｏｖａｒｌａｉ）ＤＮＡ分别经ＢａｍＨＩ,ＨｉｎｄⅢ和ＰｓｔⅠ３种内切酶酶切完全消化,通过设计１对引物,反向ＰＣＲ扩增问号赖型钩体重组质粒ｐＤＪＨ２插入片段两端的未知序列．结果显示不同酶切环化连接,经反向ＰＣＲ扩增均可得２条大小相等的扩增带．结果提示反向ＰＣＲ技术可以用于问号赖型钩体重组质粒插入片段两端的未知序列的研究,为获得钩体完整基因序列提供新的途径．     

二维稳态各向异性介质渗透率的反演问题

1.引 言由多孔介质的渗流理论,二维稳态各向异性介质的渗流问题满足下列偏微分方程 -div(u(x,y)(?)u(x,y))=f(x,y),(x,y)∈Ω(?)R2, (1.1)     

THE INVERSE PROBLEM FOR PART SYMMETRIC MATRICES ON A SUBSPACE

In this paper, the following two problems are considered:Problem Ⅰ. Given S∈E Rn×p,X,B 6 Rn×m, find A ∈ SRs,n such that AX = B, where SR8,n = {A∈ Rn×n|xT(A - AT) = 0, for all x ∈ R(S)}.Problem Ⅱ. Given A* ∈ Rn×n, find A ∈ SE such that ||A-A*|| = minA∈sE||A-A*||, where SE is the solution set of Problem Ⅰ.The necessary and sufficient conditions for the solvability of and the general form of the solutions of problem Ⅰ are given. For problem Ⅱ, the expression for the solution, a numerical algorithm and a numerical example are provided.     

Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions：Further Results

The asymptotic expansions of the trace of the heat kernel θ(t)=∑^∞v=1^exp(-tλv) for small positive t,where {λv} are the eigenvalues of the negative Laplacian -△n=-∑^ni=1(D/Dx^1)^2 in R^2(n=2 or 3),are studied for a general annular bounded domain Ω with a smooth inner boundary DΩ1 and a smooth outer boundary DΩ2,where a finite number of piecewise smooth Robin boundary conditions(D/Dnj γh)Ф=0 on the components Гj(j= 1,...,m) of (DΩ1 and on the components Гj (j=k 1,…,m) of of DΩ2 are considered such that DΩl=U^kj=lГj and DΩ2= U^m=k 1Гj and where the coefficients γj(j=1,...,m) are piecewise smooth positive functions. Some applications of θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained.     

Ranks of Solutions of the Matrix Equation AXB = C

The purpose of this article is to solve two problems related to solutions of a consistent complex matrix equation AXB = C : (I) the maximal and minimal ranks of solution to AXB = C , and (II) the maximal and minimal ranks of two real matrices X₀ and X₁ in solution X = X₀ + iX₁ to AXB = C . As applications, the maximal and minimal ranks of two real matrices C and D in generalized inverse (A + iB)^- = C + iD of a complex matrix A + iB are also examined.